The invention generally relates to digital communication and in particular to methods, systems, and computer program products for decoding a received data signal.
In recent years, wireless communication systems have grown at an accelerated pace, thereby becoming central components of modern modes of communications.
Different wireless communication systems are available today, such as the cellular and wireless ad-hoc networks accommodating single or multiple transmitters/receivers using single or multiple antennas, such as MIMO (Multiple INPUT Multiple OUTPUT) systems. A wireless MIMO communication system refers to radio links with multiple antennas at the transmitter side and at the receiver side.
The significant development of MIMO systems over scattering-rich wireless channels is due to their ability to meet the increasing needs in terms of communication reliability and data rate on wireless networks.
Many decoders have been proposed to retrieve signal streams sent over such wireless communication systems with an improved performance in terms of data rate and reliability. However, a major challenge of such decoders is the complexity cost. In order to warrant the deployment for real-time and high-throughput applications, it is desirable that the coding operations and decoding algorithms satisfy the prescribed computational complexity which is fixed for a given device and application.
For example, Maximum Likelihood (ML) decoders, such as the sphere decoder (E. Viterbo and E. Biglieri. A universal decoding algorithm for lattice codes. In Quatorzieme colloque GRETSI, 1993) or the Schnorr Euchner decoder (C. P. Schnorr and M. Euchner. Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems. In Math. Programming, pages 181-191, 1993) are optimal decoders which require an exponential complexity in the number of antennas (B. Hassibi and H. Vikalo. On the sphere-decoding algorithm i. expected complexity. Signal processing, IEEE Transactions on, 53(8):2806-2818, August 2005).
These decoders have been adapted to reduce their complexity at a possible cost of performance degradation in terms of a tradeoff between complexity and performance, according to two different approaches. In a first approach, the decoder is based on a node pruning-based tree search algorithm which is configured to discard some nodes (and their children) in each layer if they are associated with a low likelihood function to lead to the optimal solution. Exemplary decoders operating according to this first approach comprise for example:                probabilistic tree pruning sphere decoding (Byonghyo Shim and Insung Kang. Sphere decoding with a probabilistic tree pruning. Signal Processing, IEEE Transactions on, 56(10):4867-4878, October 2008; Tao Cui, Shuangshuang Han, and C. Tellambura. Probability distribution-based node pruning for sphere decoding. Vehicular Technology, IEEE Transactions on, 62(4):1586-1596, May 2013);        the k-best algorithms (Qingwei Li and Zhongfeng Wang. Improved k-best sphere decoding algorithms for mimo systems. In Circuits and Systems, 2006. ISCAS 2006. Proceedings. 2006 IEEE International Symposium on, pages 4 pp.-1162, May 2006); and        increasing radii algorithms (R. Gowaikar and B. Hassibi. Statistical pruning for near maximum likelihood decoding. Signal Processing, IEEE Transactions on, 55(6):2661-2675, June 2007).        
The second approach relates to iterative decoders. An iterative decoder is based on the equivalent channel matrix form induced from the code structure to determine partitioned signal sets to be decoded iteratively. Such iterative approach reduces the decoding complexity while not maintaining a desired error performance and full diversity.
For example, in the article “Won-Joon Choi, R. Negi, and J. M. Cioffi. Combined ML and DFE decoding for the v-blast system. In Communications, 2000. ICC 2000. 2000 IEEE International Conference on, volume 3, pages 1243-1248 vol. 3, 2000”, the channel matrix is divided into two blocks, the first block having a size q. An ML decoding scheme is performed on the first block of size q, while a decision feedback equalizer (also referred to as ZF-DFE) is applied to the remaining system given the output of the ML decoding performed on the first block (i.e. the ML output is subtracted from the received signal). Even if such solution increases the performance, the decoding is sub-optimal while not ensuring a target diversity order.
Another solution, proposed for space-time coded systems which are compatible with sphere decoders, consists in splitting the received signal into a number L (L≥2) of subsets each of a given cardinality λ. A conditional maximization of a likelihood function with respect to one of set of signal points given another is performed. This comprises:                Dividing the equivalent channel matrix into L sub-matrices with accordance to the splitting of the received signal;        Selecting, among the L sub-sets of the received signal, a signal set according to a given criterion;        For all the possible values of the remaining L−1 subsets taken from the alphabet, performing a conditional ZF (ACZF) or ZF-DFE (ACZF-SIC) detection (also referred to hereinafter as ‘decoding’) of the selected signal sub-set after removing the inter-sub-sets interference;        Selecting, among the overall calculated solutions the optimal one which corresponds to the minimization of the Euclidean distance between the received signal and the estimated one.        
The choice of the signal set to be detected (also referred to hereinafter as ‘decoded’) conditioned on the values of the remaining signal sub-sets has an impact on the performance of the algorithm. Inspired from the work disclosed in S. D. Howard, S. Sirianunpiboon, and A. R. Calderbank. Low Complexity Essentially Maximum Likelihood Decoding of Perfect Space-Time Block Codes. In Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International, a selection criterion for n×n space-time coded systems using the Perfect codes has been proposed in L. P. Natarajan and B. S. Rajan. An Adaptive Conditional Zero-Forcing Decoder with Full-diversity, Least Complexity and Essentially-ML Performance for STBCs. In Information Theory and its Applications (ISITA), 2012 International Symposium on, pages 235-239, October 2012, particularly for a 2×2 MIMO system using the Golden code, 3×3 and 4×4 configurations
Accordingly, the signal set selected in second step described above is the sub-set corresponding to the divided sub-matrix of the equivalent channel matrix of maximum determinant of covariance matrix overall divided sub-matrices. Moreover, sufficient conditions on the characteristics of the sub-matrices of the equivalent channel matrix involving characteristics of the used Space-Time Block Code have been disclosed in L. P. Natarajan and B. S. Rajan. An Adaptive Conditional Zero-Forcing Decoder with Full-diversity, Least Complexity and Essentially-ML Performance for STBCs. In Information Theory and its Applications (ISITA), 2012 International Symposium on, pages 235-239, October 2012. One of these sufficient conditions imposes that, in order to achieve a full diversity order under ACZF or ACZF-SIC decoding, at least one of the L sub-matrices should be full rank.
Although existing sub-detection methods offer better performance than sub-optimal linear and non-linear joint decoding schemes, they do not allow to control the diversity order while achieving a reduced complexity.